Title: The universal *-regular R-ring
Speaker: Sonia L'Innocente (University of Camerino)
Abstract: Olivier's construction of the universal commutative (von Neumann) regular ring over a commutative ring is generalized to obtain the universal *-regular ring over a noncommutative ring (R, *) with involution. The construction of a universal *-regular ring proceeds similarly with the Moore–Penrose inverse replacing the role of the group inverse in the construction of universal abelian regular rings.
The involution of (R, *) induces an involution on the modular lattice L(R, 1) of positive primitive formulae in the language of left R-modules. It is shown that *-regular ring coordinatizes the quotient lattice of L(R, 1) modulo the least congruence for which the involution designates an orthogonal complement.
Some explicit examples will be given in the context of some algebras, as the Jacobson algebra. This is joint work with Ivo Herzog.
URL associated with Seminar: https://research.math.osu.edu/logicseminar/
